The Puzzler #32

An advisor has four clients: Arnie, Bob, Charlie, and Diane. The values of the portfolios are as follows: $5 million, $3 million, $2 million, and zero. The clients make the following statements:

Arnie: My portfolio and Charlie’s are the biggest and smallest.

Bob: My portfolio and Arnie’s have a total of $5 million.

Charlie: If you subtract what’s in Diane’s portfolio from mine, you get $3 million.

Diane: Neither I nor Arnie have the biggest or smallest portfolios.

Two of these statements are lies. Which client has the most money in his or her portfolio?

Please e-mail your solution to John Kador at jkador@jkador.com using the subject line “On Account.” The deadline is Oct. 1, 2012. One entrant with the correct answer (or a creative alternative) will receive a signed copy of John Kador’s How to Ace the Brainteaser Job Interview. Good luck to all.

Brainteaser #2: WATER PUZZLE

You have a 4-ounce cup, a 9-ounce cup and an endless supply of water. You have no other tools. Describe the fewest number of steps required to measure exactly 6 ounces of water.

See solution at the bottom of the page.

Solution to previous puzzler: ELEVATOR MAN

To recap: A man lives on the 10th floor. From the lobby, if there is someone else waiting for the elevator, he gets off on the 10th floor. If he is alone, he gets off on the seventh floor and walks up three flights. If rain has been predicted for the day, the man always rides the elevator to floor 10. Why?

This puzzle generated the most responses of any in The Puzzler’s history: over 175. The winner is Michelle Oakley, advisor associate at Waddell & Reed in Nashville, Tenn. Michelle’s response: The man is a short person. He can only reach the button for the seventh floor. If someone else is on the elevator, he will ask that person to press the button for the 10th floor. If rain has been predicted, he will have his umbrella, which he will use to press the button for the 10th floor.

Almost everyone got it right, although we were impressed by some intricate conspiracy stories concerning an affair with a neighbor’s wife or a phobia for odd- and even-numbered floors.

Congratulations to Michelle, who will receive a signed copy of my book, How to Ace the Brainteaser Job Interview.

Solution to Water Puzzle: This classic puzzle was used in a Car Talk Puzzler. The minimum solution requires an eight-step process: 1. Fill the 9-ounce cup. 2. Pour the water from the 9-ounce cup into the 4-ounce cup, leaving 5 ounces in the larger cup. 3. Empty the 4-ounce cup. 4. From the 9-ounce cup, fill the 4-ounce cup, leaving 1 ounce in the 9-ounce cup. 5. Empty the 4-ounce cup. 6. Transfer the 1 ounce of water from the 9-ounce cup into the 4-ounce cup, which now has 1 ounce of water. 7. Fill the 9-ounce cup with water. 8. Pour water from the 9-ounce cup into the 4-ounce cup until it is full. Because the small cup already had 1 ounce of water, only 3 ounces from the larger cup will transfer, leaving 6 ounces of water in the 9-ounce cup.

Correction: A number of readers pointed out an ambiguity with the July issue’s Coin Toss problem, which had to do with the odds of someone in a crowd of 1,024 people being able to predict 10 coin tosses in a row. The printed solution said it was a sure thing. Not so fast, said Bill Jacobs, Jacobs Investment Management, Nashville, Tenn. He writes: The odds of a person correctly guessing 10 consecutive coin tosses is (1/2)^10 = 1/1024. The odds of NOT guessing correctly would be 1 – (1/1024) = 1023/1024. The odds of 1,100 people guessing incorrectly would be (1023/1024) ^ 1100 = 34%.

This calculation reverses the outcome of the puzzle. In retrospect, the wording of the puzzle was confusing and we apologize.

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